Jan 9 
Jeffrey Galkowski (NEU) 
Eigenfunctions: What are they and what do they tell us?
abstract±
We give an introduction to Laplace eigenfunctions including an overview of some of the important problems from the last century. Laplace eigenfunctions are a useful model problem in a variety of situations and their behavior can be observed in the oscillation of drum membranes, the behavior of electrons, scattering of sound waves, and many other physical systems. Towards the end of the hour, we will give a heuristic discussion of microlocal methods and results.
Poster.

Jan 16 
Alexander Moll (NEU) 
An Introduction to Dispersive Shock Waves
abstract±
At this informal talk, we will define traveling waves and dispersive shock waves of dispersive wave equations, watch experiments and simulations of them on a projector, summarize the heuristics in Whitham modulation theory, ponder what Liouville integrability should mean for wave equations, and contemplate a remarkable singular rational curve from DobrokhotovKrichever (1991).
Poster.

Jan 23 
Changho Han (Harvard) 
Modular compactifications of moduli spaces in algebraic geometry
abstract±
In this talk, we give an introduction to moduli spaces as a way to understand families of objects in consideration. Then, we will see different compactifications of moduli spaces, specially the moduli spaces of curves. If time remains, we will introduce compactifications of moduli of surfaces and their geometry.

Jan 30 
ChiYun Hsu (Harvard) 
Congruences of modular forms and the eigencurve
abstract±
One way to think about a modular form is
through its qexpansion, a power series in
q. Different modular forms can have congruent
qexpansions modulo a prime power, and this
phenomenon inspired Coleman and Mazur to
construct a geometric object called the
eigencurve. In this talk, I will illustrate
congruences of modular forms by examples. I
will also explain how the arithmetic of
modular forms translates into geometry of the
eigencurve.
Poster.

Feb 6 
Peter Hintz (MIT) 
General relativity and microlocal analysis
abstract±
The study of Einstein's field equation in general relativity leads to many interesting and challenging problems in the area of partial differential equations. I will focus on the second simplest type of solution of the field equation, black holes, and describe some questions about their nearequilibrium behavior, and interactions with other black holes. Tools from microlocal analysis and spectral theory are key to recent answers to some of these, and I will sketch how and why.
Poster.

Feb 13 
Jonathan Wang
(MIT) 
Geometric approach to local Lfactors and spherical varieties
abstract±
Recent work suggests that the theory of spherical varieties may help provide a link between period integrals and special values of automorphic Lfunctions. More specifically, the local factor of the Lfunction is related to harmonic analysis on the spherical variety. For certain spherical varieties, these Lfactors were computed at the level of functions by Sakellaridis. However for more general computations, it is expected that a more geometric (in the sense of sheaves replacing functions) approach is needed. I will explain the setup for such an approach and current efforts in this direction.
Poster.

Feb 20 
Tom Bachmann (MIT) 

Feb 27 
Eunice Kim (Tufts) 

Mar 6 
No Seminar. 
Spring Break.

Mar 13 
Euan Spence (U. Bath) 

Mar 20 
Elina Robeva (MIT) 

Mar 27 
Lynnelle Ye (Harvard) 

Apr 3 
Geoffrey Smith (Harvard) 

Apr 10 
Scott Mullane (Frankfurt) 

Apr 17 
Ana Balibanu (Harvard) 



End of Semester (Seminar Resumes Fall 2019) 